Match the equation to the parabola
Which formula belongs to the parabola in the picture?
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From a picture of a parabola you can read almost the whole formula. The vertex (m, n) gives the form y = a(x − m)² + n. Opening upward means a > 0, opening downward means a < 0. When you move 1 to the right from the vertex, the graph goes up or down by exactly a.
What does this generator do?
It draws a parabola and offers four formulas. At the easy level they differ in the signs of the shift; at the medium level also in the number a (a narrower, wider or upside-down parabola). At the hard level the formulas are expanded in the form ax² + bx + c.
How to use it
1) Find the vertex and watch the sign: the vertex (2, −1) belongs to (x − 2)² − 1. 2) Decide whether the parabola opens upward or downward. 3) Go 1 to the right from the vertex and see how far the graph goes up — that is a. 4) For the expanded form, also check the y-intercept: it is the number c.